A little more than a month after the Abbott government's tough first budget, which most voters say they still regard as ''unfair'', the Coalition is closing the gap on Labor and returning to pre-budget levels of support.

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Poll: Abbott's approval stays low

The coalition's vote has partly recovered from post-budget lows, but people still don't think much of the budget - or the Prime Minister.

The government's primary vote has surged four points in a month, but Tony Abbott's low personal standing would still have seen the federal government swept from office in an election held now, despite the Coalition closing the gap.

The mini-recovery, which follows the Prime Minister's trip to France, Canada and the United States, has wiped out some of Labor's lead but the ALP is still six points ahead after preferences, 53 per cent to 47.

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The numbers are contained in the nationwide Age/Nielsen poll of 1400 voters taken between last Thursday and Saturday, and which also found 66 per cent of voters opposed Australian military involvement to restore order in Iraq compared with 31 per cent favouring Australian participation.

Opposition Leader Bill Shorten remains the preferred prime minister by 47 per cent of voters, with Mr Abbott languishing on 40 per cent. The Labor leader also enjoys a positive net approval rating of plus-1 per cent compared to Mr Abbott on minus-25 per cent.

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Equally worrying for Mr Abbott is the finding that Malcolm Turnbull, the man he replaced as Liberal leader in 2009 by just one party-room vote, is preferred by Australians at the rate of two-to-one in a straight shootout between the two men. But the situation is almost reversed among Liberal voters, who strongly favour Mr Abbott.

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Mr Turnbull is far and away the most popular leader in a field of six Liberals, virtually doubling Mr Abbott's 21 per cent support at 40 per cent and almost quadrupling support for others mentioned, with Joe Hockey and Julie Bishop registering 11 per cent each and Christopher Pyne and Scott Morrison scoring only 3 and 2 per cent respectively.

However, the Coalition will take some comfort from the finding that its primary support at 39 per cent rebounded from the May 15-17 survey, when it had dropped to 35 per cent - its lowest since 2010. Labor's primary vote dropped three points to 37.

The poll bounce follows two weeks in which Mr Abbott was seen on nightly news bulletins strutting the world stage alongside Prince Charles and international leaders such as Britain's David Cameron, Germany's Angela Merkel and US President Barack Obama.

On a two-party-preferred basis, Labor maintained a strong lead of 53-47 over the Coalition but has lost some ground since the May survey, when it peaked at 56-44 in Labor's favour.

Mr Shorten's clear lead as preferred prime minister marks his second month in a row leading on this index, even though it coincided with a seven-point slump in his approval rating as opposition leader.

Some 35 per cent of voters approve of the way Mr Abbott is doing his job as prime minister compared with 60 per cent who disapprove - making for a net rating of minus 25, which is a three-point improvement since May 17.

Mr Shorten's approval rating stayed narrowly in positive territory - 42 per cent approved of the way he was performing, down five points, and an almost identical 41 per cent disapproved, for a net rating of plus-1 per cent.

The budget, much of which remains either blocked or has not even been introduced yet, appears to be a key factor affecting the Coalition, with six in 10 voters or 61 per cent regarding it as unfair and just a third or 33 per cent saying it is fair.

Social Services Minister Kevin Andrews admitted the delay in getting some budget measures through Parliament could result in a budget hole.

"It will have some impact on the budget if we can't get these measures through in a timely manner,'' Mr Andrews told ABC radio on Monday.

Speaking to reporters in Canberra on Monday, Mr Shorten rejected a suggestion that the poll showed public anger about the budget was cooling.

"Not at all. This is a dreadful budget," he said. "I believe the polls confirm what Australians already know, that this is an unfair budget and it's got the wrong priorities - cuts to pensions, increases in fuel taxes, cuts to family payments, cuts to schools and hospitals."

Pollster John Stirton noted that the question of fairness had been asked in the aftermath of eight of the 19 federal budgets since 1996 and that this was the first time in which a majority had marked a federal budget as unfair.

The poll will come as no surprise to Liberal and Nationals MPs who are increasingly aware of voter dissatisfaction with the budget.

While the government secured passage for its temporary 2 per cent deficit levy on top tax bracket earnings last week, several other aspects of the budget face stiff opposition in the existing Senate dominated by Labor and the Greens and in the new upper house from next month.

In a bid to force the pace, the government will push much of the legislation for measures intended to start from July 1 into Parliament this week, having tabled the legislation just days ago.